What Is \[$1 \frac{2}{3}\$\] As An Improper Fraction?A. \[$\frac{2}{3}\$\] B. \[$\frac{5}{3}\$\] C. \[$\frac{6}{3}\$\] D. \[$\frac{8}{3}\$\]
What is ${1 \frac{2}{3}\$} as an improper fraction?
Understanding Mixed Numbers and Improper Fractions
In mathematics, mixed numbers and improper fractions are two ways to express a number that is not a whole number. A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we follow these steps:
- Multiply the whole number by the denominator.
- Add the numerator to the product.
- Write the result as a fraction with the product as the numerator and the denominator as the original denominator.
Converting ${1 \frac{2}{3}\$} to an Improper Fraction
Let's apply the steps to convert ${1 \frac{2}{3}\$} to an improper fraction.
- Multiply the whole number by the denominator: 1 × 3 = 3
- Add the numerator to the product: 3 + 2 = 5
- Write the result as a fraction with the product as the numerator and the denominator as the original denominator: {\frac{5}{3}$}$
Conclusion
Therefore, ${1 \frac{2}{3}\$} as an improper fraction is {\frac{5}{3}$}$. This is the correct answer among the options provided.
Why is {\frac{5}{3}$}$ the Correct Answer?
The correct answer is {\frac{5}{3}$}$ because it is the result of converting the mixed number ${1 \frac{2}{3}\$} to an improper fraction. The steps followed to convert the mixed number to an improper fraction are accurate, and the result is {\frac{5}{3}$}$.
Common Mistakes to Avoid
When converting mixed numbers to improper fractions, it's essential to follow the correct steps to avoid mistakes. Some common mistakes include:
- Not multiplying the whole number by the denominator
- Not adding the numerator to the product
- Writing the result with the wrong numerator or denominator
Tips for Converting Mixed Numbers to Improper Fractions
To convert mixed numbers to improper fractions easily, follow these tips:
- Multiply the whole number by the denominator first
- Add the numerator to the product next
- Write the result as a fraction with the product as the numerator and the denominator as the original denominator
Real-World Applications of Converting Mixed Numbers to Improper Fractions
Converting mixed numbers to improper fractions has real-world applications in various fields, including:
- Cooking: When a recipe calls for a mixed number of ingredients, converting it to an improper fraction can make it easier to measure the ingredients accurately.
- Building: When building a structure, converting mixed numbers to improper fractions can help architects and engineers calculate the exact amount of materials needed.
- Finance: When dealing with mixed numbers of currency, converting them to improper fractions can help accountants and financial analysts calculate the exact amount of money.
Conclusion
In conclusion, converting mixed numbers to improper fractions is a crucial skill in mathematics that has real-world applications. By following the correct steps and tips, we can convert mixed numbers to improper fractions easily and accurately. The correct answer to the question is {\frac{5}{3}$}$, and it's essential to understand why it's the correct answer to avoid common mistakes.
Final Answer
The final answer is {\frac{5}{3}$}$.
Q&A: Converting Mixed Numbers to Improper Fractions
Frequently Asked Questions
In this article, we'll answer some frequently asked questions about converting mixed numbers to improper fractions.
Q: What is a mixed number?
A: A mixed number is a combination of a whole number and a fraction. For example, ${1 \frac{2}{3}\$} is a mixed number.
Q: What is an improper fraction?
A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, {\frac{5}{3}$}$ is an improper fraction.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, follow these steps:
- Multiply the whole number by the denominator.
- Add the numerator to the product.
- Write the result as a fraction with the product as the numerator and the denominator as the original denominator.
Q: Can you give an example of converting a mixed number to an improper fraction?
A: Let's convert ${1 \frac{2}{3}\$} to an improper fraction.
- Multiply the whole number by the denominator: 1 × 3 = 3
- Add the numerator to the product: 3 + 2 = 5
- Write the result as a fraction with the product as the numerator and the denominator as the original denominator: {\frac{5}{3}$}$
Q: Why is it important to convert mixed numbers to improper fractions?
A: Converting mixed numbers to improper fractions is important because it makes it easier to perform mathematical operations, such as addition and subtraction. It also helps to avoid mistakes and ensures accuracy in calculations.
Q: Can I use a calculator to convert mixed numbers to improper fractions?
A: While a calculator can be helpful, it's not necessary to convert mixed numbers to improper fractions. The steps are simple and can be done manually.
Q: Are there any common mistakes to avoid when converting mixed numbers to improper fractions?
A: Yes, some common mistakes to avoid include:
- Not multiplying the whole number by the denominator
- Not adding the numerator to the product
- Writing the result with the wrong numerator or denominator
Q: Can you give some real-world examples of converting mixed numbers to improper fractions?
A: Here are a few examples:
- Cooking: When a recipe calls for a mixed number of ingredients, converting it to an improper fraction can make it easier to measure the ingredients accurately.
- Building: When building a structure, converting mixed numbers to improper fractions can help architects and engineers calculate the exact amount of materials needed.
- Finance: When dealing with mixed numbers of currency, converting them to improper fractions can help accountants and financial analysts calculate the exact amount of money.
Q: Is there a shortcut to converting mixed numbers to improper fractions?
A: While there is no shortcut, you can use a formula to convert mixed numbers to improper fractions. The formula is:
{\frac{(a \times b) + c}{b}$}$
Where a is the whole number, b is the denominator, and c is the numerator.
Conclusion
In conclusion, converting mixed numbers to improper fractions is a crucial skill in mathematics that has real-world applications. By following the correct steps and tips, we can convert mixed numbers to improper fractions easily and accurately. If you have any more questions, feel free to ask!
Final Answer
The final answer is {\frac{5}{3}$}$.